We examine the physical properties of 173 cluster members in CL 1358+62 (z = 0.3283) from HST WFPC2 imaging taken in the F606W (∼rest-frame B) and F814W (∼rest-frame V ) filters over a 2.2×2.2 Mpc 2 field (H 0 = 100 km s −1 Mpc −1 , Ω M = 0.3, Ω Λ = 0.7). Structural parameters are measured for each galaxy by fitting a PSF-convolved, two component model to their 2D surface brightness distribution. We examine bulge+disk models using three different bulge profiles (de Vaucouleurs, Sérsic, and exponential), and rigorously test the robustness of our results by analyzing several thousand artificial galaxies in the same manner as the cluster data. The measured physical properties from the best-fit profile of the cluster galaxies are combined with ground-based spectroscopy to test for correlations between morphological characteristics, current star formation, total galaxy colors, and cluster substructure. We find that: (1) Bulge-to-total ratio [(B/T ) deV ] and Hubble type (−5 ≤ T ≤ 8) are strongly correlated (99% confidence), but the scatter is large and early-type spirals are not reliably distinguished from ellipticals and S0's based on (B/T ) deV . (2) From comparison of their physical properties, the low luminosity (−17.3 ≥ M B z − 5 log h ≥ −19.3) ellipticals in our sample are likely to be face-on S0 galaxies. (3) High galaxy asymmetry and strong [OII]λ3727 emission are strongly correlated for disk-dominated members [(B/T ) deV < 0.4].(4) There exists a small population (∼ 5%) of bulge-dominated members whose significant [OII]λ3727 emission (< −5Å) suggest they harbor active galactic nuclei. (5) At these redshifts, determining the correct Sérsic index n can be highly unreliable.